It is natural to assume that he would. Not only has he only served one term, has nationwide name recognition (if not popularity) and the ability to raise a massive campaign war chest of funds with little to no effort, but as of yet, there is apparently no viable Republican challenger that can command a majority of a national electorate.
This will not be like the 2008 election, but Obama may win simply because a majority of voters will view him as the lesser of two evils if choosing between him and Michelle Bachman or Rick Perry. If the economy goes in the tank by 2012, then all bets are off, but I don't know of any political adviser who would not tell Obama he should run again.
As I have not heard of any other democratic contender for the position, there is no reason why President Obama should not run. However, considering the state of the country, economy, and etc. people might consider him to have been ineffective and vote for another candidate.
I see no reason why Pres. Obama should not run for the presidency again in 2012. There is no obvious Democratic candidate who would clearly do better than him and so it makes sense for him to run again.
Almost every sitting president runs again for office. The last one not to even try to be reelected was Lyndon Johnson in 1968 and he had the Vietnam War disaster looming over him. Obama does not have any similar disaster (some might say the health care bill is, but a large percentage of the electorate actually likes it). Any other Democrat would have to defend the health care bill anyway and so there is no real benefit to the Democrats to have someone else run.
There is no reason for Pres. Obama not to run. His approval ratings are decent (around 50%) and there is no Republican or Democrat who is clearly more favored to win than he is.